Question

a man bought 270 oranges for Rs 25.00. Some of them at the rate of 10 a rupee and the rest at the rate of 12 a rupee. Find the no. of each kind?

Answer 1

Let us say, the man bought N oranges at the rate of 10 a Rupee, that is, each at Rs 1/10. 

He bought the remaining (270 - N) at the rate of 12 a Rupee, that is each at Rs 1/12.

Total cost of of oranges = $\\. \ \ \ N * \frac{1}{10} + (270-N) * \frac{1}{12} = Rs 25 \\ \\. \ \ \ So,\ \frac{6 * N + (270-N) * 5}{60} = Rs 25 \\ \\. \ \ \ 6N + 1350 - 5 N = 1500 \\ \\. \ \ \ N + 1350 = 1500 \\ \\. \ \ \ N = 150 \\ \\ He\ bought\ 150\ oranges\ at\ the\ rate\ of\ 10\ a \Rupee.\ \ and \\ \ \ \ the\ remaining\ 270 - 150 = 120\ oranges\ at\ \ 12\ a\ Rupee.$

Answer 2

Let the no. of orange of cost Rs 1/10 = x
no. of oranges of cost Rs 1/12 = y

so, x + y = 270 ........(1)
Cost of x oranges = Rs x/10
cost of y oranges = Rs y/12

total cost = Rs 25

x/10 + y/12 = 25  ...(2)

Multiply (2) by 12

12x/10 + y = 300

1.2x + y = 300
     x + y = 270     (subtract)
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0.2x = 30

x = 150

y = 270 - 150 = 120